Finite Group Databasebeta

← #16777387

Subgroups — #16777387

Order 3328.

248 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130720C211yesmaximal, characteristic
2#13130718C211yesmaximal, characteristic
3#13116449C211yesmaximal, characteristic
4C2×#88155C2211yescharacteristic
5#11719132—21no—
6#11719116—21no—
7D13⋊#108—21no—
8#11719092—21no—
9C22×C13×C16C411yescharacteristic, complemented
10C2×#88052C411yescharacteristic, complemented
11#11718269C412yescomplemented
12#11718267C412yes—
13#11718099—21no—
14#11718099—21no—
15C2×#6127D411yescharacteristic
16#88237—22no—
17D13⋊M16—22no—
18C22×C8×C13C2×C411yescharacteristic
19C2×#6099Q811yescharacteristic
20#88155—41no—
21#88155—41no—
22C2×#6094C2×C411yescharacteristic
23C2×#6094C2×C411yescharacteristic
24C2×C8×D13D411yescharacteristic
25C2×C8×D13D411yescharacteristic
26#88121—41no—
27#88119—41no—
28#88113—41no—
29#88107—41no—
30#88104—41no—
31#88103—41no—
32#88102—41no—
33#88101—41no—
34C2×C13×C16—21no—
35C2×C13×C16—41no—
36#88052—41no—
37C2×#6090—21no—
38#7227—131nomaximal, Sylow
39C22×C4×C13C4⋊C411yescharacteristic
40C2×C22⋊D13D811yescharacteristic
41C2×C22⋊D13Q1611yescharacteristic
42#6127—41no—
43#6127—41no—
44C2×D52SD1611yescharacteristic
45C2×C4×D13C22⋊C411yescharacteristic
46C2×C4×D13C22⋊C411yescharacteristic
47C2×Dic26SD1611yescharacteristic
48C22⋊#261—42no—
49#6122—42no—
50C4⋊#261—42no—
51C4×#261—42no—
52#6118—42no—
53D13⋊C8—42no—
54C2×C8×C13—21no—
55C2×C8×C13—21no—
56C2×C8×C13C4211yescharacteristic
57C2×C8×C13C22⋊C411yescharacteristic
58#6099—41no—
59C2×#1055C4⋊C411yescharacteristic
60C2×#1055C4⋊C411yescharacteristic
61#6094—41no—
62#6094—41no—
63C8×D13—21no—
64C8×D13—21no—
65C8×D13—21no—
66C8×D13—21no—
67C13×C16—41no—
68#6090—41no—
69#2113—131no—
70#1813—131no—
71#1812—131no—
72C23×C13#10711yescharacteristic
73C22×D13#10211yescharacteristic
74C22×D13#10311yescharacteristic
75C2×#261—82no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13#9511yescharacteristic
79C2×C4×C13#10611yescharacteristic
80C22⋊D13—41no—
81C22⋊D13—41no—
82C2×Dic13#10211yescharacteristic
83C2×Dic13#10311yescharacteristic
84D52—41no—
85C4×D13—21no—
86C4×D13—21no—
87C4×D13—21no—
88C4×D13—21no—
89Dic26—41no—
90#1057—82no—
91C8×C13—21no—
92C8×C13#9911yescharacteristic
93C8×C13#9911yescharacteristic
94#1055—21no—
95#1055—21no—
96C2×#131—131no—
97C2×M32—131no—
98C22×C16#26111yescharacteristic, complemented
99C2×#108—261no—
100#427—261no—
101#413—261no—
102#410—261no—
103C22⋊C16—261no—
104C22⋊C16—261no—
105#338—132no—
106H(3,ℤ/4)—132no—
107C22×C13—21no—
108C22×C13—41no—
109C22×C13#34011yescharacteristic
110C2×D13—21no—
111C2×D13—21no—
112C2×D13—41no—
113C2×D13—41no—
114#261—162no—
115C4×C13—21no—
116C4×C13H(3,ℤ/4)11yescharacteristic
117C4×C13#34211yescharacteristic
118Dic13—21no—
119Dic13—21no—
120C2×#41—131no—
121#131—521no—
122#131—521no—
123C2×M16—131no—
124C2×M16—131no—
125C2×M16—131no—
126C2×M16—262no—
127C22×C8—131no—
128C22×C8—131no—
129C22×C8C2×#26111yescharacteristic
130#117—262no—
131M32—521no—
132C2×C16—21no—
133C2×C16—41no—
134C2×C16—261no—
135#108—521no—
136#108—521no—
137#107—521no—
138#106—521no—
139#101—521no—
140#100—521no—
141#99—521no—
142#99—521no—
143C2×C13—21no—
144C2×C13—41no—
145C2×C13#128911yescharacteristic
146D13—41no—
147D13—41no—
148#41—521no—
149#41—521no—
150C2×Q8—131no—
151C2×D4—131no—
152C2×D4—131no—
153C2×D4—131no—
154C22×C4—131no—
155C22×C4—131no—
156C22×C4C4⋊#26111yescharacteristic
157M16—521no—
158M16—521no—
159M16—521no—
160M16—522no—
161M16—522no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—131no—
165C2×C8—131no—
166C2×C8—261no—
167C2×C8—261no—
168C2×C8—261no—
169C2×C8—261no—
170C2×C8—522no—
171C2×C8C4×#26111yescharacteristic
172C2×C8C22⋊#26111yescharacteristic
173C4⋊C4—522no—
174C22⋊C4—522no—
175C42—522no—
176C16—41no—
177C16—521no—
178C13#722711yescharacteristic, complemented, Sylow
179C23—131no—
180C23—131no—
181C23#8810211yescharacteristic
182Q8—521no—
183D4—521no—
184D4—521no—
185D4—521no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—131no—
189C2×C4—131no—
190C2×C4—261no—
191C2×C4—261no—
192C2×C4—261no—
193C2×C4—261no—
194C2×C4—1042no—
195C2×C4#8810111yescharacteristic
196C2×C4(C2×#261)⋊C411yescharacteristic
197C8—21no—
198C8—261no—
199C8—261no—
200C8—1042no—
201C8#8810711yescharacteristic
202C8#8811911yescharacteristic
203C22—21no—
204C22—41no—
205C22—261no—
206C22—261no—
207C22—521no—
208C22—521no—
209C22#1171826511yescharacteristic
210C4—21no—
211C4—261no—
212C4—261no—
213C4—2082no—
214C4#1171826711yescharacteristic
215C4#1171828911yescharacteristic
216C2—21no—
217C2—41no—
218C2—521no—
219C2—521no—
220C2#1312969911yescharacteristic
subgroupG/H
centerC4#11718267
commutatorC2×C8×C13C42
FrattiniC22×C8C2×#261
FittingC22×C13×C16C4
socleC2×C13#1289
prime radicalC2×#6127D4
cosocleC2×#88155C22
hypercenterC22×C16#261
hypocenterC13#7227
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
9. C22×C13×C16C4semidirect
10. C2×#88052C4semidirect
11. #11718269C4semidirect
98. C22×C16#261semidirect
178. C13#7227semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131307202
#131307182
#131164492
#722713